There are three types of pedals when it comes to "bypass".
Partial bypass is the most common. This is what most of the vintage pedals used. When the effect is switched off the guitar signal doesn't go through any additional circuitry, but the effect input is still connected to the guitar.
Buffered bypass is common in a lot of modern pedals. The guitar signal always goes through the pedal circuitry, even when the effect is switched off.
True bypass, when the pedal is off, provides a direct connection for the guitar signal and also disconnects the effect circuit's input from the guitar.
They all have advantages and disadvantages. IMO, the demand for true-bypass pedals is a knee-jerk reaction to (admittedly effective) marketing. Buyers aren't really sure what true bypass is, but they think they need it.
Buffered pedals can be used to isolate the guitar from a long cable run between the pedal and the amp. If the buffer is good, it will help preserve the guitar's sparkle. If the buffer is bad, it'll alter the frequency response and introduce noise. As with anything else, you usually get what you pay for...
Partial bypass always loads down the guitar a little bit. This can affect the frequency response, usually as a reduction of the high mids and presence frequencies. That loss can often be compensated with a minor tweak of the amp controls. All I can say is, it worked for Hendrix and Clapton in the late '60s, so it couldn't have been that awful...
True bypass loads down the guitar when the effect is on, and unloads it (or more precisely, loads it only with what's downstream) when the effect is off. To me, this seems like a reasonable idea if you only use one or two pedals. With a lot of pedals, or with a long cable run to the amp, you might want to put a buffer between the guitar and the first pedal. But then, once you have that buffer the benefit of true bypass is not that useful.